Point mutations as an optimal search process in biological evolution

Point mutations are pictured as jumps in a phase space representing the sequences of amino acids or nucleotides as discrete points. It is shown that this space can be given a natural metric by quantifying common physical and chemical properties of amino acid constituents in terms of a natural measure. Evolution through point mutations is simulated by the search for points in the phase space representing amino acid sequences of high survival fitness. Due to the local compactness of the distribution of these functionally allowed points in phase space any successful search procedure has characteristics qualitatively different from those in the case of a random distribution. This is demonstrated by model calculations. A specified distribution of allowed points is generated with subsequent evaluation of the success of the retrieval process as a function of the jump probabilities between lattice sites. The results of such simulations are compared with data obtained from the analysis of the DNA or mRNA sequences coding related proteins. By counting silent and expressed nucleotide replacement frequencies one can draw conclusions as to the efficacy of the natural evolutionary search processes in the phase space of amino acid sequences. There are cases, where the highest possible information gain of one bit per accepted point mutation is achieved. In general the information gain is found to be somewhat sub-maximal due to functional requirements.